Ok. So, I've been thinking about this. I have a theory. I'll put this in spoilers even though I don't think it'll pan out the way I'm thinking, lol.
First, I think the reason he introduced himself as the future Sihyun instead of Sihu is A. b/c she doesn't know Sihu exists. B. B/c as he spends time with her, it won't mess up the future relationship that she'll have with Sihyun. C. He probably assumes that they were already close, on some level, at the point when he first came back to the past. It would make it easier for her to believe him coming from somebody she's close to.
Now, for the murder...I don't think the murder is actually that dude with the scars. It's never the most obvious person in these stories. I think it's A. the short dude crushing on her with the silvery colored hair, B. Jinwu, or C. glasses goofball (I hope not though). Leaning more towards A or C. Jinwu never showing his left hand is bugging the hell out of me though. Dude that pushed her has scars though. So maybe blondie is connected?
I dunno! I love mysteries though, so all of this has become more intriguing to me than the romance. 😅 Like I said...this is just my theory, and I'm probably completely off, lol.